Dough: Combine the milk, yeast and sugar in the bowl of an electric mixer and let rest for a few minutes to proof. Mix the eggs and salt into the yeast mixture. With a dough hook, blend in the flour. Then blend in the butter by the tablespoonful. With the dough hook, knead the dough for 7 minutes, or until springy and elastic. Transfer the dough to a lightly oiled bowl, covered with plastic wrap, and set aside in a warm place until doubled in volume, about 50 minutes.
Filling: Punch down the dough. On a lightly floured surface, roll it out into an 8 by-18-inch rectangle. Brush with the melted butter and sprinkle on the sugar and cinnamon. Starting at a long side, roll the dough up into a log. Slice into 12 (1 1/2-inch-wide) rolls.
Topping: Lightly butter the bottom of a 9 by 13-inch baking pan. In a small saucepan, combine the butter and brown sugar and cook, stirring until the sugar has dissolved. Pour the mixture into the pan and sprinkle the pecan pieces over it.
Lay rolls, cut side down, in the cake pan with the topping, squeezing them in if necessary. Let rise in a warm place until doubled in volume, about 50 minutes.
Preheat oven to 350 degrees with the rack set in the middle.
Bake the rolls for 30 to 35 minutes, or until golden brown. Carefully invert onto a serving platter and let cool for just a few minutes. Break into individual buns and serve warm, with the sticky topping, and ice cream.